Generic rigidity of a bar and joint framework in the plane is determined by the Pollaczek-Geiringer-Laman Theorem. However, given special positions for the vertices, the framework can still be infinitesimally flexible. The pure condition, introduced by White & Whiteley (1983), is a polynomial in the bracket algebra whose vanishing characterizes these special positions. We will describe various computational strategies to translate the pure condition into a relation on edge coordinates.